Stochastic linear quadratic optimal control problem for systems driven by fractional Brownian motions

Abstract

SummaryThis paper is concerned with stochastic linear control systems driven by fractional Brownian motions (fBms) with Hurst parameter H∈(1/2,1) and the cost functional is quadratic with respect to the state and control variables. Here, the integrals with respect to fBms are the type of Stratonovich integrals. A stochastic maximum principle as a necessary condition of the optimal control is derived. The adjoint backward stochastic differential equation (BSDE) is driven by the fBms and its underlying standard Brownian motions. The existence and uniqueness of the solution of adjoint BSDE is proved. The explicit form of the unique optimal control is obtained.